Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } - 15 x - 54 \geq 0$$
A) $( - \infty , - 9 ] \cup [ - 6 , \infty )$
B) $( - \infty , - 9 ) \cup ( - 6 , \infty )$
C) $( - 9 , - 6 )$
D) $[ - 9 , - 6 ]$

Question

Quizplus · Accepted Answer

First, factor the quadratic inequality: $-x^2 - 15x - 54 \geq 0$ can be rewritten as $-(x + 9)(x + 6) \geq 0$. The roots are $x = -9$ and $x = -6$. Since the leading coefficient is negative, the parabola opens downwards, meaning the expression is greater than or equal to zero between the roots. Therefore, the solution in interval notation is $[ - 9 , - 6 ]$.

Solve the Inequality −x2−15x−54≥0- x ^ { 2 } - 15 x - 54 \geq 0−x2−15x−54≥0

Solve the Inequality $- x ^ { 2 } - 15 x - 54 \geq 0$